一种新的群智能算法—黏菌算法
介绍一种新的群智能算法—黏菌算法
近些年群智能算法由于其效率较高，使用方便的优点引起了广大科研者的关注与兴趣。最近看文献，温州大学的李世民（现在去复旦读研究生了）提出了一种新的群智能优化算法----黏菌算法（Slime mould algorithm）[1]。在此附上代码
算法（Matlab实现）
SMA.m
% Max_iter: maximum iterations, N: populatoin size, Convergence_curve: Convergence curve
% To run SMA: [Destination_fitness,bestPositions,Convergence_curve]=SMA(N,Max_iter,lb,ub,dim,fobj)
function [Destination_fitness,bestPositions,Convergence_curve]=SMA(N,Max_iter,lb,ub,dim,fobj)
disp('SMA is now tackling your problem')
% initialize position
bestPositions=zeros(1,dim);
Destination_fitness=inf;%change this to -inf for maximization problems
AllFitness = inf*ones(N,1);%record the fitness of all slime mold
weight = ones(N,dim);%fitness weight of each slime mold
%Initialize the set of random solutions
X=initialization(N,dim,ub,lb);
Convergence_curve=zeros(1,Max_iter);
it=1; %Number of iterations
lb=ones(1,dim).*lb; % lower boundary
ub=ones(1,dim).*ub; % upper boundary
z=0.03; % parameter
% Main loop
while it <= Max_iter
%sort the fitness
for i=1:N
% Check if solutions go outside the search space and bring them back
Flag4ub=X(i,:)>ub;
Flag4lb=X(i,:)<lb;
X(i,:)=(X(i,:).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;
AllFitness(i) = fobj(X(i,:));
end
[SmellOrder,SmellIndex] = sort(AllFitness); %Eq.(2.6)
worstFitness = SmellOrder(N);
bestFitness = SmellOrder(1);
S=bestFitness-worstFitness+eps; % plus eps to avoid denominator zero
%calculate the fitness weight of each slime mold
for i=1:N
for j=1:dim
if i<=(N/2) %Eq.(2.5)
weight(SmellIndex(i),j) = 1+rand()*log10((bestFitness-SmellOrder(i))/(S)+1);
else
weight(SmellIndex(i),j) = 1-rand()*log10((bestFitness-SmellOrder(i))/(S)+1);
end
end
end
%update the best fitness value and best position
if bestFitness < Destination_fitness
bestPositions=X(SmellIndex(1),:);
Destination_fitness = bestFitness;
end
a = atanh(-(it/Max_iter)+1); %Eq.(2.4)
b = 1-it/Max_iter;
% Update the Position of search agents
for i=1:N
if rand<z %Eq.(2.7)
X(i,:) = (ub-lb)*rand+lb;
else
p =tanh(abs(AllFitness(i)-Destination_fitness)); %Eq.(2.2)
vb = unifrnd(-a,a,1,dim); %Eq.(2.3)
vc = unifrnd(-b,b,1,dim);
for j=1:dim
r = rand();
A = randi([1,N]); % two positions randomly selected from population
B = randi([1,N]);
if r<p %Eq.(2.1)
X(i,j) = bestPositions(j)+ vb(j)*(weight(i,j)*X(A,j)-X(B,j));
else
X(i,j) = vc(j)*X(i,j);
end
end
end
end
Convergence_curve(it)=Destination_fitness;
it=it+1;
end
end
Main.m
// An highlighted block
clear all
close all
clc
N=30; % Number of search agents
Function_name='F1'; % Name of the test function, range from F1-F13
T=500; % Maximum number of iterations
dimSize = 30; %dimension size
% Load details of the selected benchmark function
[lb,ub,dim,fobj]=Get_Functions_SMA(Function_name,dimSize);
[Destination_fitness,bestPositions,Convergence_curve]=SMA(N,T,lb,ub,dim,fobj);
%Draw objective space
figure,
hold on
semilogy(Convergence_curve,'Color','b','LineWidth',4);
title('Convergence curve')
xlabel('Iteration');
ylabel('Best fitness obtained so far');
axis tight
grid off
box on
legend('SMA')
display(['The best location of SMA is: ', num2str(bestPositions)]);
display(['The best fitness of SMA is: ', num2str(Destination_fitness)]);
Initialization.m
% This function initialize the first population of search agents
function Positions=initialization(SearchAgents_no,dim,ub,lb)
Boundary_no= size(ub,2); % numnber of boundaries
% If the boundaries of all variables are equal and user enter a signle
% number for both ub and lb
if Boundary_no==1
Positions=rand(SearchAgents_no,dim).*(ub-lb)+lb;
end
% If each variable has a different lb and ub
if Boundary_no>1
for i=1:dim
ub_i=ub(i);
lb_i=lb(i);
Positions(:,i)=rand(SearchAgents_no,1).*(ub_i-lb_i)+lb_i;
end
end
Get_Functions_SMA.m
function [lb,ub,dim,fobj] = Get_Functions_SMA(F,DimValue)
switch F
case 'F1'
fobj = @F1;
lb=-100;
ub=100;
dim=DimValue;
case 'F2'
fobj = @F2;
lb=-10;
ub=10;
dim=DimValue;
case 'F3'
fobj = @F3;
lb=-100;
ub=100;
dim=DimValue;
case 'F4'
fobj = @F4;
lb=-100;
ub=100;
dim=DimValue;
case 'F5'
fobj = @F5;
lb=-30;
ub=30;
dim=DimValue;
case 'F6'
fobj = @F6;
lb=-100;
ub=100;
dim=DimValue;
case 'F7'
fobj = @F7;
lb=-1.28;
ub=1.28;
dim=DimValue;
case 'F8'
fobj = @F8;
lb=-500;
ub=500;
dim=DimValue;
case 'F9'
fobj = @F9;
lb=-5.12;
ub=5.12;
dim=DimValue;
case 'F10'
fobj = @F10;
lb=-32;
ub=32;
dim=DimValue;
case 'F11'
fobj = @F11;
lb=-600;
ub=600;
dim=DimValue;
case 'F12'
fobj = @F12;
lb=-50;
ub=50;
dim=DimValue;
case 'F13'
fobj = @F13;
lb=-50;
ub=50;
dim=DimValue;
end
end
% F1
function o = F1(x)
o=sum(x.^2);
end
% F2
function o = F2(x)
o=sum(abs(x))+prod(abs(x));
end
% F3
function o = F3(x)
dim=size(x,2);
o=0;
for i=1:dim
o=o+sum(x(1:i))^2;
end
end
% F4
function o = F4(x)
o=max(abs(x));
end
% F5
function o = F5(x)
dim=size(x,2);
o=sum(100*(x(2:dim)-(x(1:dim-1).^2)).^2+(x(1:dim-1)-1).^2);
end
% F6
function o = F6(x)
o=sum(abs((x+.5)).^2);
end
% F7
function o = F7(x)
dim=size(x,2);
o=sum([1:dim].*(x.^4))+rand;
end
% F8
function o = F8(x)
o=sum(-x.*sin(sqrt(abs(x))));
end
% F9
function o = F9(x)
dim=size(x,2);
o=sum(x.^2-10*cos(2*pi.*x))+10*dim;
end
% F10
function o = F10(x)
dim=size(x,2);
o=-20*exp(-.2*sqrt(sum(x.^2)/dim))-exp(sum(cos(2*pi.*x))/dim)+20+exp(1);
end
% F11
function o = F11(x)
dim=size(x,2);
o=sum(x.^2)/4000-prod(cos(x./sqrt([1:dim])))+1;
end
% F12
function o = F12(x)
dim=size(x,2);
o=(pi/dim)*(10*((sin(pi*(1+(x(1)+1)/4)))^2)+sum((((x(1:dim-1)+1)./4).^2).*...
(1+10.*((sin(pi.*(1+(x(2:dim)+1)./4)))).^2))+((x(dim)+1)/4)^2)+sum(Ufun(x,10,100,4));
end
% F13
function o = F13(x)
dim=size(x,2);
o=.1*((sin(3*pi*x(1)))^2+sum((x(1:dim-1)-1).^2.*(1+(sin(3.*pi.*x(2:dim))).^2))+...
((x(dim)-1)^2)*(1+(sin(2*pi*x(dim)))^2))+sum(Ufun(x,5,100,4));
end
function o=Ufun(x,a,k,m)
o=k.*((x-a).^m).*(x>a)+k.*((-x-a).^m).*(x<(-a));
end
参考文献
[1]: Li, S., Chen, H., Wang, M., Heidari, A. A., & Mirjalili, S. (2020). Slime mould algorithm: A new method for stochastic optimization. Future Generation Computer Systems.
[2]: http://www.aliasgharheidari.com/SMA.html
[3]:https://www.researchgate.net/publication/340527543_Matlab_code_of_Slime_Mould_Algorithm_SMA